A389206 Sum of all other divisors except the squarefree part applied to the numbers satisfying Euler's condition for odd perfect numbers: a(n) = A326126(A228058(n)).

73, 169, 217, 337, 361, 421, 457, 505, 721, 541, 649, 745, 793, 785, 889, 901, 1081, 1009, 1093, 1177, 1225, 1141, 1321, 1369, 1261, 1681, 1657, 1621, 1801, 2161, 1897, 1681, 1837, 1861, 2089, 1849, 2185, 2329, 2377, 2281, 2129, 2221, 2353, 2377, 2761, 2809, 2905, 4441, 2701, 3097, 3601, 3241, 2941, 3337, 3061

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..20410

Formula

a(n) = A389203(n) - A389165(n).

For all n not in A388279, a(n) = A389203(n) - A389161(n).

a(n) = A389207(n) + A228058(n).

a(n) = A325377(n) + A389208(n).

Prog

(PARI)
up_to = 20410;
isA228058(n) = if(!(n%2)||(omega(n)<2), 0, my(f=factor(n), y=0); for(i=1, #f~, if(1==(f[i, 2]%4), if((1==y)||(1!=(f[i, 1]%4)), return(0), y=1), if(f[i, 2]%2, return(0)))); (y));
A228058list(up_to) = { my(v=vector(up_to), k=0, n=0); while(k<up_to, n++; if(isA228058(n), k++; v[k] = n)); (v); };
v228058 = A228058list(up_to);
A228058(n) = v228058[n];
A326126(n) = (sigma(n)-core(n));
A389206(n) = A326126(A228058(n));

Crossrefs

Cf. A228058, A325377, A326126, A388279, A389161, A389165, A389203, A389207, A389208.

Sequence in context: A142326 A392320 A142377 * A044405 A044786 A244774

Adjacent sequences: A389203 A389204 A389205 * A389207 A389208 A389209

Keyword

nonn

Author

Antti Karttunen, Sep 29 2025

Status

approved